For the Poincaré half-space model in dimension 2, the metric evaluates on the coordinate tangent vectors \(\frac{\partial}{\partial x}, \frac{\partial}{\partial y} \in T_pM\) as \[g_p\!\left(\frac{\partial}{\partial x^i}\bigg|_p,\;\frac{\partial}{\partial x^j}\bigg|_p\right) = \frac{1}{y^2}\,\delta_{ij},\] i.e. the coordinate tangent vectors are orthogonal and each has length \(\frac{1}{y}\) — shrinking to zero as \(p\) approaches the boundary \(y\to 0\), which is what makes the space “infinitely large” near the boundary.
pub splitting: f64,。夫子对此有专业解读
，这一点在WPS下载最新地址中也有详细论述
Special cameras are needed to spot the nocturnal animals
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